This paper presents an approach for solving a nonlinear stochastic differential equations (NSDEs) using a new basis functions (NBFs). These functions and their operational matrices are used for representing matrix form of the NBFs. With using this method in combination with the collocation method, the NSDEs are reduced a stochastic nonlinear system of equations and unknowns. Then, the error ana...

This paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (TFs) in combination with the collocation method. The method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. Finally, the error analysis and some numerical examples are provided...

A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method wa...

2 Brownian Motion 6 2.1 Kolmogorov’s Continuity Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Working With Ito Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Stopping Times and Local Martingales . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Ito Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Clustering parts and machines into part families and machine cells is a major decision in the design of cellular manufacturing systems which is defined as cell formation. This paper presents a non-linear mixed integer programming model to design cellular manufacturing systems which assumes that the arrival rate of parts into cells and machine service rate are stochastic parameters and descri...

on account of the existence of uncertainty, dea occasionally faces the situation of imprecise data, especially when a set of dmus include missing data, ordinal data, interval data, stochastic data, or fuzzy data. therefore, how to evaluate the efficiency of a set of dmus in interval environments is a problem worth studying. in this paper, we discussed the new method for evaluation and ranking i...

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...